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Speed of Sound worksheet

Grades 11–12

Solve each problem and show your work. Round answers to 2 decimal places where needed.

1.
Problem 1.
- Gas: Any ideal gas (γ and M)
- Temperature (T): 28 °C
- Heat capacity ratio (γ): 1.5
- Molar mass (M): 24 g/mol
- Show speed in: Meters per second (m/s)
Find: Speed of sound
Answer
2.
Problem 2.
- Gas: Dry air (from temperature)
- Temperature (T): 16 °C
- Show speed in: Meters per second (m/s)
Find: Speed of sound
Answer
3.
Problem 3.
- Gas: Dry air (from temperature)
- Temperature (T): 18 °C
- Show speed in: Meters per second (m/s)
Find: Speed of sound
Answer
4.
Problem 4.
- Gas: Dry air (from temperature)
- Temperature (T): 24 °C
- Show speed in: Kilometers per hour (km/h)
Find: Speed of sound
Answer
5.
Problem 5.
- Gas: Any ideal gas (γ and M)
- Temperature (T): 24 °C
- Heat capacity ratio (γ): 1.1
- Molar mass (M): 29 g/mol
- Show speed in: Miles per hour (mph)
Find: Speed of sound
Answer
6.
Problem 6.
- Gas: Dry air (from temperature)
- Temperature (T): 22 °C
- Show speed in: Meters per second (m/s)
Find: Speed of sound
Answer
7.
Problem 7.
- Gas: Any ideal gas (γ and M)
- Temperature (T): 24 °C
- Heat capacity ratio (γ): 2
- Molar mass (M): 24 g/mol
- Show speed in: Miles per hour (mph)
Find: Speed of sound
Answer
8.
Problem 8.
- Gas: Any ideal gas (γ and M)
- Temperature (T): 22 °C
- Heat capacity ratio (γ): 1.7
- Molar mass (M): 24 g/mol
- Show speed in: Miles per hour (mph)
Find: Speed of sound
Answer
9.
Problem 9.
- Gas: Any ideal gas (γ and M)
- Temperature (T): 20 °C
- Heat capacity ratio (γ): 1
- Molar mass (M): 24 g/mol
- Show speed in: Miles per hour (mph)
Find: Speed of sound
Answer
10.
Problem 10.
- Gas: Dry air (from temperature)
- Temperature (T): 13 °C
- Show speed in: Meters per second (m/s)
Find: Speed of sound
Answer

Answer key: Speed of Sound worksheet

1. Speed of sound: 395.59 m/s
1. Put the temperature in kelvins, a scale that starts at absolute zero: add 273.15
  $28 °C + 273.15$ $= 301.15 K$
2. Convert the molar mass to kg/mol, the unit the formula needs: divide by 1,000
  $\frac{24}{1,000}$ $= 0.024 kg/mol$
3. Use the ideal-gas formula, with T in kelvins and the gas constant R = 8.314462618 J/(mol·K): v = √(γ × R × T ÷ M)
  $\sqrt{\frac{1.5 \times 8.314462618 \times 301.15}{0.024}}$ $= 395.592942 m/s$
2. Speed of sound: 340.87 m/s
1. Use the dry-air formula. Start from 331.3 m/s, the speed at 0 °C, and scale it up for warmer air: v = 331.3 × √(1 + T ÷ 273.15), with T in °C
  $331.3 \times \sqrt{1 + \frac{16}{273.15}}$ $= 331.3 \times \sqrt{1.05857587}$ $= 340.865017 m/s$
3. Speed of sound: 342.04 m/s
1. Use the dry-air formula. Start from 331.3 m/s, the speed at 0 °C, and scale it up for warmer air: v = 331.3 × √(1 + T ÷ 273.15), with T in °C
  $331.3 \times \sqrt{1 + \frac{18}{273.15}}$ $= 331.3 \times \sqrt{1.06589786}$ $= 342.041837 m/s$
4. Speed of sound: 1,243.97 km/h
1. Use the dry-air formula. Start from 331.3 m/s, the speed at 0 °C, and scale it up for warmer air: v = 331.3 × √(1 + T ÷ 273.15), with T in °C
  $331.3 \times \sqrt{1 + \frac{24}{273.15}}$ $= 331.3 \times \sqrt{1.08786381}$ $= 345.548252 m/s$
2. Change the answer to km/h, the unit you picked: divide by 0.277777777778
  $\frac{345.548252}{0.277777777778}$ $= 1,243.973708 km/h$
5. Speed of sound: 684.79 mph
1. Put the temperature in kelvins, a scale that starts at absolute zero: add 273.15
  $24 °C + 273.15$ $= 297.15 K$
2. Convert the molar mass to kg/mol, the unit the formula needs: divide by 1,000
  $\frac{29}{1,000}$ $= 0.029 kg/mol$
3. Use the ideal-gas formula, with T in kelvins and the gas constant R = 8.314462618 J/(mol·K): v = √(γ × R × T ÷ M)
  $\sqrt{\frac{1.1 \times 8.314462618 \times 297.15}{0.029}}$ $= 306.127471 m/s$
4. Change the answer to mph, the unit you picked: divide by 0.44704
  $\frac{306.127471}{0.44704}$ $= 684.78765 mph$
6. Speed of sound: 344.38 m/s
1. Use the dry-air formula. Start from 331.3 m/s, the speed at 0 °C, and scale it up for warmer air: v = 331.3 × √(1 + T ÷ 273.15), with T in °C
  $331.3 \times \sqrt{1 + \frac{22}{273.15}}$ $= 331.3 \times \sqrt{1.08054183}$ $= 344.383414 m/s$
7. Speed of sound: 1,015 mph
1. Put the temperature in kelvins, a scale that starts at absolute zero: add 273.15
  $24 °C + 273.15$ $= 297.15 K$
2. Convert the molar mass to kg/mol, the unit the formula needs: divide by 1,000
  $\frac{24}{1,000}$ $= 0.024 kg/mol$
3. Use the ideal-gas formula, with T in kelvins and the gas constant R = 8.314462618 J/(mol·K): v = √(γ × R × T ÷ M)
  $\sqrt{\frac{2 \times 8.314462618 \times 297.15}{0.024}}$ $= 453.747596 m/s$
4. Change the answer to mph, the unit you picked: divide by 0.44704
  $\frac{453.747596}{0.44704}$ $= 1,015.004464 mph$
8. Speed of sound: 932.63 mph
1. Put the temperature in kelvins, a scale that starts at absolute zero: add 273.15
  $22 °C + 273.15$ $= 295.15 K$
2. Convert the molar mass to kg/mol, the unit the formula needs: divide by 1,000
  $\frac{24}{1,000}$ $= 0.024 kg/mol$
3. Use the ideal-gas formula, with T in kelvins and the gas constant R = 8.314462618 J/(mol·K): v = √(γ × R × T ÷ M)
  $\sqrt{\frac{1.7 \times 8.314462618 \times 295.15}{0.024}}$ $= 416.924413 m/s$
4. Change the answer to mph, the unit you picked: divide by 0.44704
  $\frac{416.924413}{0.44704}$ $= 932.633351 mph$
9. Speed of sound: 712.87 mph
1. Put the temperature in kelvins, a scale that starts at absolute zero: add 273.15
  $20 °C + 273.15$ $= 293.15 K$
2. Convert the molar mass to kg/mol, the unit the formula needs: divide by 1,000
  $\frac{24}{1,000}$ $= 0.024 kg/mol$
3. Use the ideal-gas formula, with T in kelvins and the gas constant R = 8.314462618 J/(mol·K): v = √(γ × R × T ÷ M)
  $\sqrt{\frac{1 \times 8.314462618 \times 293.15}{0.024}}$ $= 318.681183 m/s$
4. Change the answer to mph, the unit you picked: divide by 0.44704
  $\frac{318.681183}{0.44704}$ $= 712.869504 mph$
10. Speed of sound: 339.09 m/s
1. Use the dry-air formula. Start from 331.3 m/s, the speed at 0 °C, and scale it up for warmer air: v = 331.3 × √(1 + T ÷ 273.15), with T in °C
  $331.3 \times \sqrt{1 + \frac{13}{273.15}}$ $= 331.3 \times \sqrt{1.0475929}$ $= 339.092129 m/s$